{
  "aliases": [
    "family-set-theory",
    "index-sets",
    "indexing-set"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nIn mathematics, an **index set** is a [[set|0BSJ7RQ9BW]] whose members label (or index) members of another set. For instance, if the elements of a set $A$ may be *indexed* or *labeled* by means of the elements of a set $J$, then $J$ is an index set. The indexing consists of a [[surjective function|01RVCMSN5N]] from $J$ onto $A$, and the indexed collection is typically called an *indexed family*, often written as $\\{A_{j}\\}_{j\\in J}$.\n",
  "commit": "4a3290d299c8b2cd6493fce2296920ba7f82d942",
  "front": {
    "aliases": [
      "family-set-theory",
      "index-sets",
      "indexing-set"
    ],
    "inventory": [
      "7MD5K07DB7"
    ],
    "kind": "concept",
    "name": "Index set",
    "same_as": {
      "wikidata": "Q21285678",
      "wikipedia": "Index set"
    },
    "sources": [
      {
        "locator": "Index set",
        "mention": "wikipedia://en/393055",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:393055@r1350537554"
      }
    ],
    "tag": "RHF0MXBMBT"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/RHF0MXBMBT/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/RHF0MXBMBT.md",
  "msc": null,
  "name": "Index set",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/RHF/RHF0MXBMBT.md",
  "status": null,
  "tag": "RHF0MXBMBT",
  "uri": "m2://RHF0MXBMBT",
  "url": "https://math2.tamnd.com/wiki/index-set/",
  "writing": {
    "tag": "RHF0MXBMBT",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}